The value of $\left( {{{2.}^1}{P_0} - {{3.}^2}{P_1} + {4^3}{P_2}......{\rm{upto}}{\mkern 1mu} {\mkern 1mu} {\rm{51th}}{\mkern 1mu} {\mkern 1mu} {\rm{term}}} \right){\rm{ + }}\left( {{\rm{1}}! - {\rm{2}}!{\rm{ + 3}}!...{\rm{upto}}{\mkern 1mu} {\mkern 1mu} {\rm{51th}}{\mkern 1mu} {\mkern 1mu} {\rm{term}}} \right)$ is equal to

JEE MATHEMATICS MCQ: PERMUTATIONS

1 Easy

1 of 1

Analyzing +4 | -1

The value of

\left( {{{2.}^1}{P_0} - {{3.}^2}{P_1} + {4^3}{P_2}......\mathrm{upto}{\mkern 1mu} {\mkern 1mu} \mathrm{51th}{\mkern 1mu} {\mkern 1mu} \mathrm{term}} \right)\mathrm{ + }\left( {\mathrm{1}! - \mathrm{2}!\mathrm{ + 3}!...\mathrm{upto}{\mkern 1mu} {\mkern 1mu} \mathrm{51th}{\mkern 1mu} {\mkern 1mu} \mathrm{term}} \right)

is equal to

View answer and explanation

Correct option: C

1 + (52)!

Option C (

1 + (52)!

) is correct because by simplifying the expression using properties of permutations and factorials, the result is

1 + (52)!